Pure and applied reflections on the reduced Maxwell-Bloch system.

摘要

We consider a reduced Maxwell-Bloch system with permanent dipole, and obtain a Lax pair representation, the Bäcklund transformation and the solitons solutions. Then we show, that this particular reduced Maxwell-Bloch system can be viewed as one among an infinite hierarchy of commuting systems. We obtain analytical formulae for the hamiltonians of each system in the hierarchy, and establish the conservation laws that govern the dynamics, and coupling between the potentials of the reduced Maxwell-Bloch system, and the potentials of the higher systems.